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Describing Transformations of Quadratic Functions

Describing Transformations of Quadratic Functions 1.3 - Solution

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We want to match the given function with its graph. We will begin by noticing that the given function is a transformation of the form y=a(xh)2+k,y=a(x-{\color{#0000FF}{h}})^2+{\color{#009600}{k}}, where h{\color{#0000FF}{h}} represents a horizontal translation and k{\color{#009600}{k}} represents a vertical translation. y=x2+1\begin{gathered} y=x^2+{\color{#009600}{1}} \end{gathered} In our case, we have k=1.{\color{#009600}{k}}={\color{#009600}{1}}. This means that the graph of y=x2+1y=x^2+1 is obtained by translating the graph of y=x2y=x^2 up by 1{\color{#009600}{1}} unit.
Parent Function\text{Parent Function}

Translation\text{Translation}

Therefore, the correct answer is option C.